Concerning a (possible) spherical curve
Suppose the Earth is a sphere and latitude and longitude
are noted Bj,Lj. Between points P0==B0,L0 and P1==B1,L1
there is a point Pm==Bm,Lm such that latitude Bm is the
arithmetic mean of the other two, Bm = (B0+B1)/2, and
arc P0 to Pm is equal to arc Pm to P1; "arc" taken to mean
geodesic or shorter great-circle arc.
What I wonder is if this point lies on a curve that could be
described as follows: the locus of points Px joining P0 to
P1 on the surface of the sphere such that for latitude Bx,
where B0-Bx = n*(Bx-B1), the arc P0 to Px is n times the
arc Px to P1. "Arc" is again the shorter great-circle arc.
Is there always an Lx to make this curve possible? Can
it be a continuous curve between any two P0, P1? Is it
a known curve with a classical name?
.
Relevant Pages
- Re: Concerning a (possible) spherical curve
... arc P0 to Pm is equal to arc Pm to P1; ... P1 on the surface of the sphere such that for latitude Bx, ... Is there always an Lx to make this curve possible? ... on the same meridian of longitude, ...
(sci.math) - Re: Concerning a (possible) spherical curve
... arc P0 to Pm is equal to arc Pm to P1; ... P1 on the surface of the sphere such that for latitude Bx, ... Is there always an Lx to make this curve possible? ... the ratio of arc-lengths can never in general equal the ratio ...
(sci.math) - Re: sin x / x tends to 1...
... >>>polygon stuff, which we can regard as mere detail, you (and one or two ... But if you think about what it is saying, ... >arc length and the length of the "ruler" will become insignificant. ... It's saying that the length of a certain curve is ...
(sci.math) - Re: Area and volume of solid of revolution
... Because we do not need to know the arc length of a curve ... you mean integrating the formula ... Let's find the volume of a unit sphere and the ...
(sci.math) - Re: arc length of quadratic curve
... the point is that if you know how to measure arc length of a straight ... Can we not think of a curve as a series of connected straight line segments? ... divisions we get a better approximation and in the limit one has the "true" ... can I use the same function for quadratic curve also or what can be ...
(comp.graphics.algorithms) |
|
